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Rings Over Which Every Simple Module is Rationally Complete

Published online by Cambridge University Press:  20 November 2018

S. H. Brown
S. H. Brown*
Affiliation:
Auburn University, Auburn, Alabama
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In 1958, G. D. Findlay and J. Lambek defined a relationship between three R-modules, A ≦ B(C), to mean that A ⫅ B and every R-homomorphism from A into C can be uniquely extended to an irreducible partial homomorphism from B into C. If A ≦ B(B), then B is called a rational extension of A and in [5] it is shown that every module has a maximal rational extension in its injective hull which is unique up to isomorphism. A module is called rationally complete provided it has no proper rational extension.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 693 - 701
Copyright
Copyright © Canadian Mathematical Society 1973

References

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